Finite Group Databasebeta

D8×Dic499 #44543181

order31936
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×Dic499

Splittings

SylowC499 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D499
commutatorC4×C499C22×C4
FrattiniC2×C4C22×D499
Fitting, prime radicalC2×D8×C499C2
socleC22×C499C2×D4
cosocleC2×C4×C499C23
hypercenterC2×D8D499
hypocenterC499C4×D8
LCSG ▷ C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15968

Conjugacy classes & character table

3514 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 632);